Are there good techniques for creating high poly regions within lower poly meshes when using subdivision modifier?
So the rules for good subdivision topology, which you're violating and which are responsible for your artifacts, are:

Quads only-- no ngons, and minimal triangles.
No 6+ poles.
Put 3 and 5 poles on the most planar parts of your mesh-- definitely not at places where your mesh has a right angle.

There are other rules.  The rules only really matter for non-planar faces-- for faces that are out-of-plane with their neighboring faces-- because any verts created in the middle of a planar neighborhood will still be in-plane, and it doesn't much matter where exactly in the face they get created.  (As long as you don't have any concave faces-- when you subdivide a concave face, the subdivision-generated vert might not actually be in the bounds of your face, leading to double of the mesh and z-fighting.)
One way that good subdiv topology is sometimes communicated is, &quot;Follow your edge flow.&quot;  If you look at the top of your circle in N2RPm.png, you can see that you're just laying a grid over your circle and bridging to the edge.  &quot;Follow the edge flow&quot; isn't always very useful advice for beginners, because it's something that doesn't make sense for a while, maybe not until you're good at topo anyways, but that's a good example of not following your edge flow.
Now, given those rules, how do we bridge areas of dense verts with areas of sparse verts?  Something like this:

Notice something especially important: I bridge the higher vert count to the lower count in a planar part of the mesh.  Not where the mesh bends 90 degrees.  Notice, no ngons, no triangles.  All 3 and 5 poles are placed on planar parts of the mesh.
There are limits to bridging like this.  You can drop two verts, or multiples of that, every time you use a new edge loop.  Here, I'm bridging 16 verts to 8 verts.  But you cannot ever drop one vert-- you cannot ever, using pure quads, bridge an even number of verts to an odd number of verts.